I asked specifically about WWI because it was the next major war the US was in that involved mass conscription, but don't feel the need to exclude relevant data from previous conflicts.
EDIT: Just for clarification, I'm asking if these improvements, if any, can be linked to the NRA's efforts. In other words, was the NRA successful in its founding mission at the time?
I’m going to do a little copying/pasting from some of the submissions from Heller. They refer more to the Civilian Marksmanship Program than the NRA, but both had similar goals.
http://www.scotusblog.com/wp-content/uploads/2008/02/07-290_amicus_majgenaltenburg.pdf
And, with the nation on the brink of entering the First World War, Congress, in the Army Appropriations Act for Fiscal Year 1916-17, Pub. L. No. 64-242, 39 Stat. 619, promoted private marks- manship in three significant ways. First, Congress appropriated funds to construct shooting galleries that would be open to “organized rifle clubs.” Second, it appropriated an additional $3,000,000 for “ammunition, targets, target materi- als, and other accessories [as] may be issued for small-arms target practice and instruction of able- bodied males capable of bearing arms . . . ” At the time, this was an enormous sum, given that the entire defense budget for FY 1916-17 was $377 million. See William J. Durch & Pamela L. Reed, The Boundaries of Choice: Domestic Con- straints on Decisions Affecting the Armed Forces in THE AMERICAN MILITARY IN THE 21ST CENTURY 113 (Barry M. Blechman et al. eds., 1993). And third, it authorized the President to appoint a Director ofCivilian Marksmanship who would be responsible for developing and implementing programs to promote “marksmanship” amongst the citizenry through “the purchase of materials, supplies, and services.” 39 Stat. at 648.
Thus, the idea of a citizenry familiar with marksmanship before joining the military being a boon to national defense was not the purview of just the NRA, but the US government put some serious dollars behind it. The CMP is no longer the Dept. of the Army organization it used to be, but there are holdovers, such as the requirement that military shooting ranges be made available to civilians.
Of course, just because it is believed does not mean it is true. From further down the report: In the early 1960s, the Army commissioned a study to determine the efficacy of the DCM program. The study, undertaken by the Arthur D. Little Com- pany under the direction of former General James Gavin, concluded that those who were involved in the programs operated by the Office of the Director of the Civilian Marksmanship, when compared to those who were not, (i) had fewer casualties in battle, (ii) were more likely to use their weapons in battle, (iii) qualified in training more quickly with small arms, (iv) learned how to field strip their weapons and learned the essential nomenclature of gun components more quickly, and (v) were able to clear jammed or obstruc- tive weapons more rapidly. See ARTHUR D. LITTLE, A STUDY OF THE ACTIVITIES AND MISSIONS OF THE NBPRP, REPORT TO THE DEPARTMENT OF THE ARMY (Jan. 1966) (“Little Report”) cited in James Biser Whisker, The Citizen-Soldier Under Federal and State Law, 94 W. VA. L. REV. 947, 969-70 (1992). The Little Report revealed that while 13.1% of ordinary recruits quali- fied as “Expert,” the highest category of marksman- ship, 68.6% of recruits who had been DCM participants qualified as “Expert.” Little Report at 18 (Table II-1). The Report confirmed what common sense and nearly a millennium of military history have consistently taught: soldiers with superior training and practice are superior in battle. See Little Report at 23-24 (“the more marksmanship instruction . . . the more effective . . . in combat and the fewer the casualties”).
A related brief by retired military officers (for obvious reasons, active military don’t get involved in these sorts of things) can be found here. http://www.scotusblog.com/wp-content/uploads/2008/02/07-290_amicus_retiredmilitary.pdf
Importantly, the report found that brief training periods—such as basic training—are not as effective at boosting performance as lifelong training: “Many studies suggest that it is the accumulation of training over a lifetime that has the largest effect on individual performance, rather than simply training in the previous six months.” Id. The implication for marksmanship training is clear: service members who have lifelong experience and training in handling firearms are likely to perform better in marksmanship and other firearms skills than those who only receive firearms instruction upon entering military service.
So, although I don’t know if there is any empirical data for the period 1870-1916, there is a demonstrated correlation of capability with previous experience in later years, which was the presumption many worked under at the pre-WW1 times.